, Volume 81, Issue 3, pp 283–312 | Cite as

Gibbs' paradox and non-uniform convergence

  • K. G. Denbigh
  • M. L. G. Redhead


It is only when mixing two or more pure substances along a reversible path that the entropy of the mixing can be made physically manifest. It is not, in this case, a mere mathematical artifact. This mixing requires a process of successive stages. In any finite number of stages, the external manifestation of the entropy change, as a definite and measurable quantity of heat, isa fully continuous function of the relevant variables. It is only at an infinite and unattainable limit thata non-uniform convergence occurs. And this occurs when considered in terms of the number of stages together with a ‘distinguishability parameter’ appropriate to the particular device which is used to achieve reversibility. These considerations, which are of technological interest to chemical engineers, resolve a paradox derived in chemical theory called Gibbs' Paradox.


Continuous Function Chemical Engineer Finite Number Successive Stage Entropy Change 
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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • K. G. Denbigh
    • 1
    • 2
  • M. L. G. Redhead
    • 1
    • 2
  1. 1.Department of History and Philosophy of Science King's College (KQC)University of LondonU.K.
  2. 2.Department of History and Philosophy of ScienceUniversity of CambridgeCambridgeU.K.

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